If you are looking for adjectives that describe all three of them, I would start with shallow. All three have a clear idea of what they want, and they care very little about what it takes to get it or who they hurt along the way. They are not deeply affected by loyalty or morality and as long as they can get what they want, they don't care what anyone else has.

Another simple adjective to describe all three is wealthy. Though Jordan's wealth is not entirely clear, she would not be welcome in the circles she runs in without some money behind her.

To describe them singly, I would suggest that Tom is cruel, Daisy is practical, and Jordan is dishonest.

Jordan, Tom and Daisy, along with Nick, are often grouped together, especially by Tom, but also by Nick, though he sometimes removes himself from the grouping. The four are a "set." According to Tom, they are all "Nordic," an elusive and—even by the 1920s, according to Nick—dated "racial" category that aligns with being of northern European extraction. All run in similar social circles, at least peripherally, even if Jordan and Nick don't have the vast wealth of the Buchanans. Nick and Jordan are hardly poor: Nick is able to pursue stockbroking without apparently having to make much money, as his father has set him up, while Jordan is able to pursue a professional golf career that seems to leave her with a vast amount of leisure time to spend at dinners and parties. All four in this set are attractive, relatively young, socially at ease and used to privilege.

Tom, according to Nick, is somewhat mentally limited, arrogant and abrasive. He's racist and also looks down on "new money." Daisy is intelligent—intelligent enough to mock Tom for his racism and to hope their daughter will be a fool. Daisy is also flirtatious, dissatisfied and weak. She takes the easy way out of difficult situations. Jordan is an enigma: Nick labels her dishonest, but it's not clear whether he or she is the more dishonest party (after all, he misleads the girlfriend back in Chicago who Tom and Daisy think he's engaged to marry). Jordan's main attribute is her coolness, her unflappability. She is always lifting her chin up as if to balance a golf ball on it while emotions flare all around her. She is not one to let her emotions show.